David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
History and Philosophy of Logic 29 (1):63-81 (2008)
It is controversial whether Wittgenstein's philosophy of mathematics is of critical importance for mathematical proofs, or is only concerned with the adequate philosophical interpretation of mathematics. Wittgenstein's remarks on the infinity of prime numbers provide a helpful example which will be used to clarify this question. His antiplatonistic view of mathematics contradicts the widespread understanding of proofs as logical derivations from a set of axioms or assumptions. Wittgenstein's critique of traditional proofs of the infinity of prime numbers, specifically those of Euler and Euclid, not only offers philosophical insight but also suggests substantive improvements. A careful examination of his comments leads to a deeper understanding of what proves the infinity of primes
|Keywords||No keywords specified (fix it)|
|Categories||categorize this paper)|
|Through your library||Configure|
Similar books and articles
Denys A. Turner (2011). A Partially Skeptical Response to Hart and Russell. [REVIEW] In Michał Heller & W. H. Woodin (eds.), Infinity: New Research Frontiers. Cambridge University Press.
C. J. G. Wright (2001). Rails to Infinity: Essays on Themes From Wittgenstein's Philosophical Investigations. Harvard University Press.
Edward Nelson (2011). Part II. Perspectives on Infinity From Mathematics : 2. The Mathematical Infinity / Enrico Bombieri ; 3. Warning Signs of a Possible Collapse of Contemporary Mathematics. [REVIEW] In Michał Heller & W. H. Woodin (eds.), Infinity: New Research Frontiers. Cambridge University Press.
Hong LI & Donghui HAN (2007). What is "the Ineffable" Exactly? An Extensive Reading of Wittgenstein's Tractatus Logico-Philosophicus. Frontiers of Philosophy in China 2 (3):402 - 411.
Crispin Wright (ed.) (2001). Rails to Infinity. Harvard University Press.
Wolfgang Achtner (2011). Part I. Perspectives on Infinity From History : 1. Infinity as a Transformative Concept in Science and Theology. In Michał Heller & W. H. Woodin (eds.), Infinity: New Research Frontiers. Cambridge University Press.
Michael Heller (2011). Part IV. Perspectives on Infinity From Physics and Cosmology : 7. Some Considerations on Infinity in Physics / Carlo Rovelli ; 8. Cosmological Intimations of Infinity / Anthony Aguirre ; 9. Infinity and the Nostalgia of the Stars/ Marco Bersanelli ; 10. Infinities in Cosmology. [REVIEW] In Michał Heller & W. H. Woodin (eds.), Infinity: New Research Frontiers. Cambridge University Press.
Anthony Birch (2007). Waismann's Critique of Wittgenstein. Analysis and Metaphysics 6 (2007):263-272.
Alexandra Shlapentokh (2002). On Diophantine Definability and Decidability in Some Rings of Algebraic Functions of Characteristic. Journal of Symbolic Logic 67 (2):759-786.
Added to index2010-08-10
Total downloads26 ( #55,364 of 1,004,690 )
Recent downloads (6 months)1 ( #64,743 of 1,004,690 )
How can I increase my downloads?